布巴克尔多項式

布巴克尔多項式编辑

在數學中,布巴克尔 多項式 [1]有两种常见定义。第一种是 :

 

有时也会使用另一种定义,可以通过递归的方式进行定义。首先,规定前三 个布巴克尔多项式为:

 

然后运用下面的递推关系得到更高阶的多项式。

 

布巴克尔 多項式也可以用母函数表示 :

 

产生了许多整数序列在On-Line Encyclopedia of Integer Sequences (OEIS)[2] e PlanetMath.

生成解编辑

布巴克尔 多項式的通解為 :

 


微分操作代表编辑

布巴克尔 多項式亦可記為 :

 

用途编辑

布巴克尔 多項式的 用途:


参考文献编辑

  1. ^ Oyodum, OD; Awojoyogbe, OB; Dada, MK.; Magnuson, JN, On the earliest definition of the 布巴克尔 polynomials, Eur. Phys. J. Appl. Phys.: 21201–21202 [永久失效連結]
  2. ^ Sequences A135929 and A135936 by Neil J. A. Sloane, A137276 , Roger L. Bagula , Gary Adamson,A138476, A. Bannour, A137289, A136256, A136255 , R. L. Bagula 在 On-Line Encyclopedia of Integer Sequences
  3. ^ Book:Cryogenics: Theory, Processes and Applications, Chapter 8: Cryogenics Vessels Thermal Profilng Using the 布巴克尔 Polynomials Expansion Scheme Investigation , Editor: Allyson E.Hayes 
  4. ^ B. Dubey, T.G. Zhao, M. Jonsson, H. Rahmanov, A solution to the accelerated-predator-satiety Lotka–Volterra predator–prey problem using 布巴克尔 polynomial expansion scheme, Journal of Theoretical Biology (Elsevier), {{doi:10.1016/j.jtbi.2010.12.002}} 
  5. ^ A. Milgeam, The stability of the 布巴克尔 polynomials expansion scheme (BPES)-based solution to Lotka–Volterra problem, Journal of Theoretical Biology (Elsevier), {{doi:10.1016/j.jtbi.2010.01.026}} 
  6. ^ H. Koçak, A. Yıldırım, D.H. Zhang, S.T. Mohyud-Din, The Comparative 布巴克尔 Polynomials Expansion Scheme (BPES) and Homotopy Perturbation Method (HPM) for solving a standard nonlinear second-order boundary value problem, Mathematical and Computer Modelling(Elsevier), {{doi:10.1016/j.mcm.2011.02.031 }} 
  7. ^ A. Yildirim, The 布巴克尔 polynomials expansion scheme for solving nonlinear science problems, (PDF), The 7th International Conference on Differential Equations and Dynamic Systems, University of South Florida, Tampa, Fmorida USA, 15-18 December 2010 <Page 40 >, (原始内容 (PDF)存档于2011年7月22日) 
  8. ^ Paul Barry, Aoife Hennessy, Meixner-Type Results for Riordan Arrays and Associated Integer Sequences, Chapter 6: The 布巴克尔 polynomials (PDF), Journal of Integer Sequences (JIS) 
  9. ^ H. Koçak, Z. Dahong, A. Yildirim, A range-free method to determine antoine vapor-pressure heat transfer-related equation coefficients using the 布巴克尔 polynomials expansion scheme, Russian Journal of Physical Chemistry A, Focus on Chemistry (Springer) [永久失效連結]
  10. ^ H. Koçak, Z. Dahong, A. Yildirim, Analytical expression to temperature-dependent Kirkwood-Fröhlich dipole orientation parameter using the 布巴克尔 Polynomials Expansion Scheme (BPES), Indian Journal of Physics(Springer) [永久失效連結]
  11. ^ A. Belhadj, O. F. Onyango and N. Rozibaeva, 布巴克尔 Polynomials Expansion Scheme-Related Heat Transfer Investigation Inside Keyhole Model (PDF), Jornal of Thermophysics and Heat Transfer (American Institute of Aeronautics and Astronautics) AIAA) [永久失效連結]
  12. ^ D. H. Zhang, Study of a non-linear mechanical system using 布巴克尔 polynomials expansion scheme BPES, International Journal of Non-Linear Mechanics(Elsevier) 
  13. ^ Emna Gargouri-Ellouze, Noreen Sher Akbar, Sohail Nadeem, Modelling Nonlinear Bivariate Dependence Using the 布巴克尔 Polynomials Copula The 布巴克尔 polynomials (PDF), Studies in Nonlinear Sciences (SNS) 
  14. ^ W. X. Yue, H. Koçak, D. H. Zhang , A. Yıldırım, A second attempt to establish an analytical expression to steam-water dipole orientation parameter using the 布巴克尔 polynomials expansion scheme, Journal of Structural Chemistry (Springer) [永久失效連結]
  15. ^ D. H. Zhang, L. Naing, The 布巴克尔 polynomials expansion scheme BPES for solving a standard boundary value problem (PDF), Applied Sciences,(Balkan Society of Geometers, Geometry Balkan Press) 
  16. ^ A. Belhadj, J. Bessrour, M. Bouhafs and L. Barrallier, Experimental and theoretical cooling velocity profile inside laser welded metals using keyhole approximation and 布巴克尔 polynomials expansion, Journal of Thermal Analysis and Calorimetry(Akadémiai Kiadó, Springer Science & Kluwer Academic Publishers B.V.), {{doi:10.1007/s10973-009-0094-4 }} [永久失效連結]
  17. ^ S. Amir Hossein A. E. Tabatabaei, T. Gang Z., O. Bamidele A. and Folorunsho O. Moses, Cut-off cooling velocity profiling inside a keyhole model using the 布巴克尔 polynomials expansion scheme, Heat and Mass Transfer(Springer Berlin / Heidelberg), Volume 45, Number 10 / août 2009, pages:1247-1251 {{doi:10.1007/s00231-009-0493-x}} [永久失效連結]
  18. ^ S. Fridjine and M. Amlouk, A NEW PARAMETER-ABACUS FOR OTIMIZING PV-T HYBRID SOLAR DEVICES FUNCTIONAL MATERIALS USING 布巴克尔 POLYNOMIALS EXPANSION SCHEME, Modern Physics Letters B ([ISSN: 0217-9849, by WS: World Scientific Publishing Co Pte Ltd] ) 
  19. ^ T. G. Zhao, Y. X. Wang and K. B. Ben Mahmoud, Limit and uniqueness of the 布巴克尔-Zhao polynomials single imaginary root sequence, International Journal of Mathematics and Computation, ISSN 0974-5718, (原始内容存档于2011-08-13) 
  20. ^ Luzon, A.; Moron, M., RECURRENCE RELATIONS FOR POLYNOMIAL SEQUENCES VIA RIORDAN MATRICES, Pages 24-25: 布巴克尔 POLYNOMIALS associated Riordan matrix (PDF) 
  21. ^ B. Tirimula Rao, P. Srinivsu, C. Anantha Rao, K. Satya Vivek Vardhan, Jami Vidyadhari ,Page 8 : 布巴克尔 polynomials
  22. ^ Kiliç Bülent, Erdal Bas, Page 7, Citation 27: 布巴克尔 polynomials

外部链接编辑

a New Parameter:. AN Abacus for Optimizing Pv-T Hybrid Solar Device Functional Materials Using the 布巴克尔 多項式 Expansion Scheme  and [1]
De Khawarizmi à Euler, La Presse Magazine, January 9, 2008  (法文), vedi anche tunisie7arts.com
Le polynôme de 布巴克尔 (PDF), La Presse Magazine, April 22, 2007, (1019): 6 [永久失效連結] (法文)
A new polynomial sequence... The 布巴克尔 Polynomials, Numerical Methods for Partial Differential Equations NMPDE [永久失效連結]
Solution to Heat Equation Using 布巴克尔 Polynomials (PDF), J. of Thermophysics and Heat Transfer [永久失效連結]
布巴克尔 多項式 Weak Solutions to a Robin Boundary Conditioned Dynamic-State Heat Transfer Problem, International Journal of Heat Transfer 
  • WS World Scientific Publishing Co Pte Ltd
AMLOUK–布巴克尔 EXPANSIVITY..USING 布巴克尔 多項式, Functional Materials Letter 
  • Pubblicazioni accademiche
A new polynomial sequence ...The 布巴克尔 Polynomials, International Journal of Applied Mathematics 
  • 其他文件:
., Journal of Crystal Growth 
., Current appied physics 
Sciendedirect.com: . , . , . ,., Journal of Alloys and Compounds ,. . ,. , . , ., Material Letters , ., Thermochimica Acta 
  • ENEA Ente Nazionale per le Energie Alternative
An attempt... using 布巴克尔 多項式, International Journal of Heat and Technology 
Numerical Distribution of Temperature During Welding Using 布巴克尔 Polynomials, Numerical Heat Transfer, Part A, Applications 
Establishment of an Ordinary Generating Function and a Christoffel-Darboux Type First-Order Differential Equation for the Heat Equation Related 布巴克尔-Turki Polynomials (PDF), Journal of Differential Equations and C.P. 
Some new properties of the applied-physics related 布巴克尔 polynomials (PDF)